an open tank has the shape of a right circular cone. the tank is 5ft across the top and 20ft high. how much work is done in emptying the tank by pumping the water to a height of 10ft above the top edge? use 62.5 lb/ft^3 for water

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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an open tank has the shape of a right circular cone. the tank is 5ft across the top and 20ft high. how much work is done in emptying the tank by pumping the water to a height of 10ft above the top edge? use 62.5 lb/ft^3 for water

Expert Solution
Step 1

Given that the tank is 5 ft across the top and 20 ft high. 

Let r be the radius of an infinitesimal small disk at any intermediate height y. Then

ry=520r=14y

The volume of an infinitesimal small disk with height y and thickness dy is

dv=Area×Thickness=πr2dy=π16y2dy

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